Hamilton-Jacobi (HJ) equation is a
class of nonlinear hyperbolic partial differential equations that
have wide applications in optimal control, geometric optics, image
processing and computer graphics, etc. In this talk I will present
an efficient iterative method, the fast sweeping method, for computing
the numerical solution of static convex HJ equations on both structured
and unstructured meshs. Convergence, error estimate and optimal
complexity will be shown. Every iterative method converges for a
reason. The fast sweeping method can converge in a finite number
of iterations that is independent of mesh size. I will explain the
two most crucial mechanisms, ordering and causality enforcement during
Gauss-Seidel iterations, for the fast convergence of fast sweeping
method. Applicability of the fast sweeping method to other
hyperbolic type problems will also be discussed.